Wow, really? What volume/page does he define this termin-ology?
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Niel de BeaudrapAug 30 '11 at 1:06

1

I just looked it up. He describes it precisely for the purpose of contrasting with the factorial function, and the name seems to be a play on words (term-inal rather than factor-ial). I was suspicious that he would give such prominence to such an elementary bit of mathematics, but it makes sense in the name of pedagogy.
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Niel de BeaudrapAug 30 '11 at 10:41

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It's not terminal, it's termial. It also doesn't matter why he put it in his books, it is exactly what the questioner was asking about.
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tlehmanAug 30 '11 at 12:38

2

ah, then I managed to misread it several times. Also –– if you will forgive me –– I was somewhat skeptical that Knuth would deign to give this function a name (especially when I thought that name was supposed to be "terminal", which made little sense to me); I wanted to see for myself, and also see why he would do so.
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Niel de BeaudrapAug 30 '11 at 12:41

3

@Niel: concerning "for pedagical reasons": I'd say, the additive analogon of a "factor" in a multiplication is "summand", so then it should rather be called "summorial" or "summatorial"
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Gottfried HelmsOct 4 '11 at 6:14

These numbers are also called the triangular numbers. You might think of the triangular numbers as naming a sequence: 1, 3, 6, 10, 15, 21,... But a sequence of integers is really just a function from $\mathbb{N}$ to $\mathbb{Z}$, so the triangular numbers also name the function you've written above.
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Jonas KibelbekAug 29 '11 at 20:59